MATLAB Implementation of Gray GM(1,1) Model with Modular Function Design

The Gray GM(1,1) model discussed here is designed as a callable function in MATLAB. The implementation features detailed intermediate comments that clearly explain each computational step, including the accumulation generation operation (AGO), parameter estimation using least squares method, and time response sequence calculation. This well-documented structure enables straightforward modifications to create other gray system algorithms by adjusting core components like the whitening equation or background values. The function accepts input data sequences and returns predicted values with model accuracy metrics. Key algorithm steps include: 1. Data preprocessing and validity checks 2. Construction of accumulated generation sequence 3. Parameter estimation through matrix operations (using MATLAB's backslash operator for efficient computation) 4. Generation of predicted values via the GM(1,1) time response function By integrating additional variables and datasets with this foundational model, users can develop more sophisticated hybrid models for complex problem-solving scenarios. The object-oriented implementation approach allows inheritance and extension for building enhanced gray prediction models with higher precision and adaptability to various practical applications.